Rounding Calculator
Rounding Modes
Standard (Half Up)
Round 0.5 and above up, below 0.5 down
Round Up (Ceiling)
Always round toward positive infinity
Round Down (Floor)
Always round toward negative infinity
Banker's (Half Even)
Round 0.5 to nearest even number
Common Rounding Examples
Related Calculators
Understanding Rounding
What is Rounding?
Rounding is the process of reducing the number of digits in a number while keeping its value close to the original. It's used to simplify numbers, reduce precision to match measurement accuracy, or present data in a more readable format.
Rounding Methods
Standard Rounding (Half Up)
The most common method. Round up if the next digit is 5 or greater.
Round Up (Ceiling)
Always round toward positive infinity.
Round Down (Floor)
Always round toward negative infinity.
Banker's Rounding (Half Even)
Round 0.5 to nearest even number to reduce bias.
Rounding to Different Places
| Original | Decimal Places | Result |
|---|---|---|
| 3.14159 | 4 | 3.1416 |
| 3.14159 | 2 | 3.14 |
| 3.14159 | 0 | 3 |
| 1234.5 | -1 (tens) | 1230 |
| 1234.5 | -2 (hundreds) | 1200 |
When to Use Each Method
Rounding Error Warning
Rounding always introduces some error. When performing multiple calculations, round only at the final step to minimize accumulated error. This is especially important in scientific and financial applications.
Frequently Asked Questions
What is the standard rounding rule?
Standard rounding (also called 'round half up') looks at the digit after your rounding position. If it's 5 or greater, round up. If it's less than 5, round down. For example, 2.35 rounded to one decimal place becomes 2.4, while 2.34 becomes 2.3.
What is banker's rounding?
Banker's rounding (round half to even) rounds 0.5 to the nearest even number instead of always rounding up. This reduces cumulative rounding errors. For example, 2.5 rounds to 2, but 3.5 rounds to 4. Both round to even numbers.
When should I use round up vs round down?
Use round up (ceiling) when you need to ensure you have enough of something - like materials for a project. Use round down (floor) when you need to stay under a limit - like fitting items in a container. Standard rounding is best for general accuracy.
How do I round to significant figures?
Significant figures counting starts from the first non-zero digit. To round 0.004567 to 2 significant figures, find the first two significant digits (4 and 5), then round based on the next digit (6): result is 0.0046.